Is there anything resembling differential calculus over the space of (nicely behaved) regions in $\mathbb{R}^d$, where addition is interpreted in terms of Minkowski sums? For example, it is known that Minkowski sums act linearly on the perimeter of two-dimensional convex bodies. Is there any se...

I'm considering a set which is described by the intersection of two convex sets in a discrete domain. We assume that the sum of elements of each vector is the same. For instance, $S = \{(2, 2, 2, 2), (3, 2, 2, 1), (2, 3, 2, 1), (2, 2, 3, 1), (3, 2, 3, 0)\}$ is not convex set in a discrete sense b...

I'm considering a set which is described by the intersection of two convex sets in a discrete domain. We assume that the sum of elements of each vector is the same. For instance, $S = \{(2, 2, 2, 2), (3, 2, 2, 1), (2, 3, 2, 1), (2, 2, 3, 1), (3, 2, 3, 0)\}$ is not convex set in a discrete sense b...